Circles/Transcript
Transcript Text reads: The Mysteries of Life starring Tim and Moby Tim is cooking pancakes while Moby is sitting at the table. TIM: Do you want one pancake or two? MOBY: Beep TIM: Don't think we have enough batter for 50 pancakes. An animation shows a spatula placing two pancakes on a plate. MOBY: Beep. Tim reads from a typed letter. TIM: Dear Tim & Moby, what exactly is a circle; and how do you measure one? From, Dylan. Circles, eh? MOBY: Beep. An animation shows a pattern of different geometric figures. TIM: Well, Moby, a circle is a little more complicated than a polygon. An image shows a plate sitting on the pattern. Two pancakes are on the plate. An animation shows the pattern transforming into a table cloth. TIM: For one thing, a circle has only one side. In mathematics, it's known as being a closed curve. An animation shows Moby's hand grabbing the two pancakes off of the plate. The plate is now empty. TIM: We define a circle as the set of all points in a plane that are the same distance from one particular point in the plane. An image shows a dot in the center of the plate. An animation shows the plate being surrounded by dots. MOBY: Beep? An animation shows Moby's hand pointing at the dot in the center of the plate. Moby begins to tap the dot. TIM: Well, that point is called the center. If we know a circle's center, then we can measure all sorts of stuff about the circle. MOBY: Beep. TIM: Well, I'll show you. The diameter of a circle is the distance across the circle through its center. An animation shows a dotted line traveling across the plate. The line travels through the dot in the center of the plate. TIM: What's the diameter of your plate? An animation shows Moby using a measuring tape to measure his plate. MOBY: Beep. TIM: Okay, the diameter of our circle is 26 centimeters. The radius is the distance from the center to any point on the circle. An image shows a plate. Across the plate, a dotted line is shown. The line travels through the center of the plate and is labeled "26". An animation shows red dots moving from the dot in the center of the plate to the edge of the plate. MOBY: Beep. TIM: Right, the radius is one-half of the diameter. And our radius is 13 cm. An animation shows the red dots rotating around the circle until they land on top of the dotted line that is traveling across the circle. The red dots are labeled "13". MOBY: Beep. TIM: The circumference of the circle is its perimeter, or the distance around the circle. An animation shows a plate being surrounded by dots. TIM: We can find the circumference by using the formula c equals pi times the diameter. An animation shows Moby's hand pointing at the symbol for pi. MOBY: Beep. TIM: Well, pi is a constant often represented by this symbol. Tim points to the symbol for pi. TIM: It's a funny little number, but for some reason it's really useful in measuring circles. An animation shows the symbol for pi. Behind the symbol, a non-terminating decimal is appearing one digit at a time. TIM: As far as we know, it goes on forever, but in most cases it’s okay to round it off to 3.14. 3.14 times 26 equals 81.64, and that’s our circumference, more or less. An animation shows a plate. Across the plate, a dotted line is shown. The line travels through the center of the plate and is labeled "26". Dots are shown surrounding the plate. TIM: If we wanted to get really precise, we could say that the circumference is 26pi and leave it at that. An animation shows Moby holding up a sign that reads "26 pi". MOBY: Beep. TIM: Well, the area covered by the circle is known as the disk. We can find the area of the disk with another equation. The formula for area is a, area, equals pi times the radius squared. An image shows a striped plate. A dotted line is drawn from its center to its edge. The line is labeled "13" and also "r". TIM: We plug in our radius, and get a equals pi times 13 squared. Order of operations says that we square the 13 first, and 13 squared (or 13 times 13) equals 169. And 169 times 3.14 equals 530.66. If we round to the nearest whole number, that's 531 square centimeters! See all the stuff we can learn armed with just a reasonable approximation of pi and the center of a circle? What are you… MOBY: Beep! An animation shows Moby holding a nail in one hand and a hammer in the other hand. TIM: Marking the center of the circle. I see. An animation shows Moby hammering the nail into the center of the circle. TIM: I suppose it's pretty safe to assume that I'm getting blamed for this. MOBY: Beep. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts